Finite Group Databasebeta

← #29575877

Subgroups — #29575877

Order 15616.

478 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455635C211yesmaximal, characteristic
2#21454384C211yesmaximal, characteristic
3#21444503C211yesmaximal, characteristic, complemented
4C2×#16839510C211yesmaximal, characteristic, complemented
5#21444207C211yesmaximal, characteristic
6#21443693C211yesmaximal, characteristic, complemented
7C61×#1301C211yesmaximal, characteristic, complemented
8C2×#14519783—21no—
9C2×#14519777C2211yescharacteristic
10C4×#11758222C2211yescharacteristic
11#16840058—21no—
12#16840053—21no—
13#16840048C412yes—
14#16840043C412yes—
15#16839804—21no—
16#16839788—21no—
17#16839787—22no—
18#16839786C2211yescharacteristic
19#16839784—21no—
20C2×C4⋊#92418C2211yescharacteristic
21C4⋊C8×D61—21no—
22#16839764—21no—
23#16839510—21no—
24#16839510—21no—
25#16839509—22no—
26#16839494—21no—
27#16839491—21no—
28C61×#431C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C2×C4⋊C8×C61C2211yescharacteristic
31C2×#11758222D411yescharacteristic
32C22×Dic122—21no—
33#14519783—42no—
34#14519783—42no—
35C2×#11758194—21no—
36C2×#11758189—22no—
37C22×#92418—21no—
38C2×C8×D61—22no—
39#14519777—21no—
40#14519777—21no—
41#14519777—21no—
42#14519777C2×C412yes—
43C4×Dic122C2×C411yescharacteristic
44C4×Dic122D411yescharacteristic
45C4×D244C2×C411yescharacteristic
46C4×D244D411yescharacteristic
47C4×C22⋊D61—21no—
48C4×C22⋊D61—21no—
49#14519736D411yescharacteristic
50#14519734—21no—
51C2×C4⋊Dic61—21no—
52C2×C4⋊Dic61—21no—
53C42×D61—21no—
54#14519711—22no—
55#14519709—22no—
56C4⋊#92418—21no—
57C4⋊#92418—21no—
58C4⋊#92418—21no—
59C4⋊#92418D412yes—
60#14519706—22no—
61#14519706—22no—
62#14519702—22no—
63#14519699—22no—
64C2×M16×C61—21no—
65C22×C8×C61—21no—
66C2×C42×C61C2311yescharacteristic
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70C4⋊C8×C61C2×C412yes—
71C4⋊C8×C61D411yescharacteristic
72C4⋊C8×C61D411yescharacteristic
73C22⋊C8×C61—21no—
74C4×C8×C61—21no—
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61#4111yescharacteristic
77C22×C4×C61#4111yescharacteristic
78C2×C22⋊D61—21no—
79C22×Dic61—41no—
80#11758222—21no—
81#11758222—21no—
82#11758222SD1612yes—
83#11758222Q1612yes—
84C2×D244C22⋊C411yescharacteristic
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×Dic122—22no—
89C2×Dic122—41no—
90C2×Dic122—82no—
91C2×Dic122C22⋊C411yescharacteristic
92M16×C61—41no—
93M16×C61—41no—
94C2×C8×C61—22no—
95C2×C8×C61—21no—
96C2×C8×C61—21no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C42×C61C22×C411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C22⋊Dic61—21no—
105#11758198—21no—
106#11758198—21no—
107C4⋊Dic61—22no—
108C4⋊Dic61—22no—
109C4⋊Dic61—41no—
110C4⋊Dic61—41no—
111C4⋊Dic61C22⋊C411yescharacteristic
112C4⋊Dic61C22⋊C411yescharacteristic
113#11758196—21no—
114#11758196—21no—
115C4×Dic61—21no—
116C4×Dic61—21no—
117C4×Dic61—21no—
118#11758194—41no—
119#11758194—41no—
120C2×#92418—22no—
121C2×#92418—41no—
122C2×#92418—81no—
123#11758189—44no—
124C8×D61—44no—
125C23×C61#12311yescharacteristic
126C22×D61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—41no—
130C2×C4×C61C2×C22⋊C411yescharacteristic
131C2×C4×C61C4×D411yescharacteristic
132C2×C4×C61C4×D411yescharacteristic
133C2×C4×C61#12011yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12111yescharacteristic
136C2×C4×C61C2×SD1611yescharacteristic
137C2×C4×C61C2×Q1611yescharacteristic
138C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C61#13711yescharacteristic
140C22⋊D61—22no—
141C22⋊D61—22no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—42no—
146C2×Dic61—82no—
147D244—21no—
148D244#10312yes—
149C4×D61—22no—
150C4×D61—22no—
151C4×D61—41no—
152C4×D61—41no—
153C4×D61—81no—
154Dic122—21no—
155Dic122—82no—
156Dic122—82no—
157Dic122#10312yes—
158C8×C61—42no—
159C8×C61—41no—
160C8×C61—41no—
161C8×C61—81no—
162#92418—42no—
163#92418—81no—
164#9169—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61#38611yescharacteristic
168C22×C61#48311yescharacteristic
169C22×C61#48411yescharacteristic
170C2×D61—22no—
171C2×D61—41no—
172C2×D61—41no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61C2×#10311yescharacteristic
177C4×C61#41711yescharacteristic
178C4×C61#45011yescharacteristic
179C4×C61#45111yescharacteristic
180C4×C61#47111yescharacteristic
181C4×C61#47311yescharacteristic
182Dic61—22no—
183Dic61—41no—
184Dic61—41no—
185Dic61—82no—
186#3079—611no—
187#2906—611no—
188#1549—611no—
189C2×#333—611no—
190#1477—611no—
191#1301D6111yescharacteristic, complemented
192#1292—611no—
193C2×C61—21no—
194C2×C61—21no—
195C2×C61#187211yescharacteristic
196C2×C61#190311yescharacteristic
197C2×C61#190811yescharacteristic
198D61—42no—
199C2×#131—1221no—
200C2×C4⋊Q8—611no—
201C4×#41—611no—
202#477—1221no—
203#476—1221no—
204#475—612no—
205#474—612no—
206#431C2×D6111yescharacteristic
207#428—1221no—
208#424—1222no—
209#424—1221no—
210#423—611no—
211#423—1221no—
212#423C2×D6111yescharacteristic
213C2×C4⋊C8—611no—
214C2×C4⋊C8—1221no—
215C2×C4⋊C8C2×D6111yescharacteristic
216#417—1221no—
217#333—1221no—
218#333—1221no—
219#332—1222no—
220Q8⋊C8—1221no—
221D4⋊C8—1221no—
222C61#916911yescharacteristic, complemented, Sylow
223C2×#41—611no—
224C22×Q8—1221no—
225#131—2442no—
226#131—2442no—
227C2×M16—21no—
228C2×M16—1222no—
229C2×M16—1221no—
230C22×C8—21no—
231C22×C8—1222no—
232C22×C8—1221no—
233C4⋊Q8—612no—
234C4⋊Q8—1221no—
235C4⋊Q8—1221no—
236C4⋊Q8—1221no—
237C4×Q8—611no—
238C4×Q8—611no—
239C4×D4—611no—
240C4×D4—611no—
241C4×D4—1221no—
242C4×D4—1221no—
243#117—611no—
244#117—1221no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C42—1221no—
248C2×C42C22×D6111yescharacteristic
249#107—1222no—
250#106—1222no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—612no—
255C4⋊C8—1222no—
256C4⋊C8—1222no—
257C4⋊C8—1221no—
258C4⋊C8—1221no—
259C4⋊C8—1221no—
260C4⋊C8C4×D6112yes—
261C4⋊C8D24411yescharacteristic
262C4⋊C8D24411yescharacteristic
263#103—1222no—
264#102—1222no—
265C22⋊C8—21no—
266C4×C8—21no—
267#41—612no—
268#41—612no—
269#41—1221no—
270#41—1221no—
271C2×Q8—611no—
272C2×Q8—1222no—
273C2×Q8—4882no—
274C2×Q8—2441no—
275C2×D4—611no—
276C2×D4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—2441no—
281C22×C4#1175822211yescharacteristic
282C22×C4D4×D6111yescharacteristic
283C22×C4#1175822611yescharacteristic
284M16—41no—
285M16—41no—
286M16—2444no—
287M16—2441no—
288M16—2441no—
289C2×C8—22no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—1222no—
296C2×C8—4881no—
297C2×C8—2444no—
298C2×C8—2441no—
299C4⋊C4—611no—
300C4⋊C4—611no—
301C4⋊C4—1221no—
302C4⋊C4—1221no—
303C4⋊C4—1222no—
304C4⋊C4—1222no—
305C4⋊C4—2441no—
306C4⋊C4—2441no—
307C22⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C42—1221no—
311C42—1221no—
312C42—1221no—
313C42C2×C4×D6111yescharacteristic
314C42C2×D24411yescharacteristic
315C42D4×D6111yescharacteristic
316C42D4×D6111yescharacteristic
317C23—1221no—
318C23#1451976211yescharacteristic
319Q8—612no—
320Q8—1221no—
321Q8—4882no—
322Q8—4882no—
323D4—612no—
324D4—1222no—
325D4—1222no—
326D4—1221no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—1221no—
331C2×C4—1222no—
332C2×C4—1222no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—4881no—
336C2×C4—4882no—
337C2×C4—2442no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4C22⋊C4×D6111yescharacteristic
341C2×C4#1451973911yescharacteristic
342C2×C4C4×D24411yescharacteristic
343C2×C4#1451974711yescharacteristic
344C2×C4#1451975011yescharacteristic
345C2×C4#1451975211yescharacteristic
346C2×C4SD16×D6111yescharacteristic
347C2×C4Q16×D6111yescharacteristic
348C2×C4#1451980111yescharacteristic
349C2×C4#1451980611yescharacteristic
350C8—42no—
351C8—41no—
352C8—41no—
353C8—81no—
354C8—4881no—
355C8—2442no—
356C22—21no—
357C22—21no—
358C22—1222no—
359C22—2441no—
360C22—2441no—
361C22#1683964011yescharacteristic
362C22#1684009411yescharacteristic
363C22#1684009911yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—1222no—
368C4—4882no—
369C4—2441no—
370C4—2441no—
371C4#103×D6111yescharacteristic
372C4#1683976011yescharacteristic
373C4#1683991411yescharacteristic
374C4#1683991911yescharacteristic
375C4#1684002611yescharacteristic
376C4#1684003811yescharacteristic
377C2—21no—
378C2—21no—
379C2—2442no—
380C2#2144612511yescharacteristic
381C2#2144629811yescharacteristic
382C2#2144633311yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1301C2
socleC22×C61#386
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1301D61
hypocenterC61#9169
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1301

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #21444503C2semidirect
4. C2×#16839510C2semidirect
6. #21443693C2semidirect
7. C61×#1301C2semidirect
191. #1301D61semidirect
222. C61#9169semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214556352
#214543842
#214445032
C2×#168395102
#214442072
#214436932
C61×#13012
#916961